A Fuzzy-SOM Method for Fraud Detection in Power Distribution Networks with High Penetration of Roof-Top Grid-Connected PV

energies

Article A Fuzzy-SOM Method for Fraud Detection in Power Distribution Networks with High Penetration of Roof-Top Grid-Connected PV

Alireza Vahabzadeh 1 , Alibakhsh Kasaeian 1,*, Hasan Monsef 2 and Alireza Aslani 1

1 Faculty of New Sciences and Technologies, University of Tehran, Tehran 1439957131, Iran; [email protected] (A.V.); [email protected] (A.A.) 2 School of Electrical and Computer Engineering, University of Tehran, Tehran 1417414418, Iran; [email protected] * Correspondence: [email protected]; Tel.: +98-912-194-7510; Fax: +98-21-884-97324

Received: 2 February 2020; Accepted: 4 March 2020; Published: 10 March 2020

Abstract: This study proposes a fuzzy self-organized neural networks (SOM) model for detecting fraud by domestic customers, the major cause of non-technical losses in power distribution networks. Using a bottom-up approach, normal behavior patterns of household loads with and without photovoltaic (PV) sources are determined as normal behavior. Customers suspected of energy theft are distinguished by calculating the anomaly index of each subscriber. The bottom-up method used is validated using measurement data of a real network. The performance of the algorithm in detecting fraud in old electromagnetic meters is evaluated and veriﬁed. Types of energy theft methods are introduced in smart meters. The proposed algorithm is tested and evaluated to detect fraud in smart meters also.

Keywords: fraud-detection; non-technical loss; power distribution; load proﬁle modeling; data mining; fuzzy-SOM

1. Introduction Power grids fall into three main sectors of production, transmission and distribution. A large portion of the power grid losses belongs to distribution networks due to their expansiveness, speed of development and inappropriate operation. In 2018, 10.79% of the electricity delivered to Iran’s national grid was lost in distribution. That is equivalent to a stunning amount of 32 billion kWh [1]. Generally, electrical energy losses are the portion of electricity that is injected into the transmission and distribution grid but is not paid for by end-users. In other words, part of the electricity injected into the transmission and distribution grid, which does not generate any revenue for the electricity providers, is called loss of electricity. Electricity losses consist of two main components, namely “technical losses” and “non-technical losses”. Technical losses occur due to the current passing through the inherent characteristic of electrical resistance of the conductors of the grid. These types of losses are found in transmission and distribution lines, transformers and metering systems. Non-technical losses originate from oﬀ-system activities and occur in various forms, including electricity theft, non-payment by subscribers, and errors in recording and calculating energy costs. An important issue facing the problem of losses in electricity distribution networks is the serious challenge of unclear share of technical and non-technical losses in the networks. Calculated technical losses are not reliable because of insuﬃcient information, poor quality of equipment, poor installation quality and low operational quality. Introduction of small-scale generators into the grid, and especially small domestic solar units, as well as wind mini-generators, micro-hydro generators, etc. has increased the complexity

Energies 2020, 13, 1287; doi:10.3390/en13051287 www.mdpi.com/journal/energies Energies 2020, 13, 1287 2 of 24 of assessing electrical energy losses, especially in the non-technical sector. The conventional rule of detecting non-technical losses in power distribution companies includes field visiting and testing customer meters. The aforementioned methods result in less detection of those subscribers who disrupt their meters at certain times but for the whole metering period. The non-technical losses imposed on the power grid thus account for a significant share of total non-technical losses. In addition, the high number of customers and the need to test all network meters make these methods very costly. In practice, in many cases the high cost of testing equipment, the cost of manpower and the cost of transporting swallows a large portion of the revenue from non-technical loss recovery. Numerous studies have so far provided useful solutions to detect such fraud. A method for detecting fraud by high-voltage customers is presented in [2,3]. The methods presented in these studies are based on artificial intelligence and data mining and have achieved successful results. Another interesting research work is that of Monedero et al. [4]. The proposed method based on artificial neural networks was used in the Spanish Seville power grid, and the remarkable result was a 50% improvement in the detection of non-technical casualties compared to previous methods. In general, methods for detecting non-technical losses and unauthorized use of the power grid can be divided into three categories: theoretical methods, hardware methods and data analysis methods [5]. Among these, data-analysis-based methods have the highest share, which in practice are preferred over other methods because of the high cost of meter testing or installation of consumption monitoring hardware. Numerous proposed and tested methods have had significant results in monitoring and reducing technical losses, but technological changes such as smart grids techniques and technologies [6], digital meter technology, and the development of domestic energy generation using on-grid rooftop photovoltaic (PV) panels have created complexities in non-technical loss-detection models. Various articles have focused on the detection of non-technical losses and unauthorized use of the network in smart networks [6–9], but the issue of non-technical losses in networks with large numbers of grid-connected small scale generations has been considered in few research works. The effect of such resources on non-technical losses of distribution grids, has received less attention in the literature. Expanding the use of almost no-cost solar/mini-wind/micro-hydro power (apart from initial investment costs) will generally encourage a minimal use of the costly network energy, but the problem arises when there are similarities between the behavior of subscribers suspected of manipulating meters and subscribers using these small resources. This similarity of consumption behavior makes it difficult to distinguish these two types of subscribers using the methods presented in previous research. This study focuses on rooftop grid-connected solar resources, where the model may be extended to mini-wind and micro-hydro generation using the relevant resource models. There are also some other small-scale resource technologies such as small parabolic solar collectors which are mostly used for heating and cooking, hence are not included in the study. The basic goals of this study can be summarized as follows:

Accelerating detection and control of non-technical losses of distribution networks. • Controlling the cost of detecting non-technical losses in power distribution companies. • Providing an efficient model for consumption management. • Modeling the effect of renewable resource development on customers’ load behavior. • Modeling the non-technical losses of distribution networks in this study is fully consistent with a variety of conventional energy theft methods. The comprehensive model presented is applicable to a wide range of distribution networks, both traditional and modern smart distribution networks, which has received little research attention. Customers’ energy consumption is measured using modern smart meters in the Iranian power distribution network, but there are still significant numbers of electromagnetic or old digital meters in the network. Due to the differing data resolution available in traditional meters and smart meters, the detection method of non-technical losses of these two types of subscribers is different in some stages. The method presented in this study is based on data-mining models. Since some subscribers who have Energies 2020, 13, 1287 3 of 24 successfully passed the meter test process may also have attempted energy theft, the consumption data of the verified meters alone cannot provide a precise pattern of customer consumption behavior. We use a bottom-up approach to determine the electrical energy consumption pattern. Electrical load profiles are generated for customers with and without rooftop photovoltaic resources. The proposed bottom-up model simulates the random behavior of the customers and, thus, the load profile may be different from one customer to another. The effect of rooftop PV on load profile is then. This study considers photovoltaic systems equipped with maximum power point tracking (MPPT). A method based on self-organized neural networks (SOM), is proposed to detect suspected subscribers to fraud and consumption anomalies. The model is then evaluated in a real sample network.

2. Modeling Domestic Load Profile We need to know the behavior of loads, and in particular, domestic customers in this study. Some studies of power distribution networks such as master planning, loss reduction studies and protection coordination studies use cumulative models of load behavior. A common method of analyzing load behavior is to measure the simultaneous power consumption of a number of customers of a particular category (e.g., domestic, commercial, industrial, etc.) and extend it to other customers of the same category using coincidence factors [10]. The factor decreases as the number of subscribers increases. Examples of coincidence curves are given in different references such as in [11]. The peak demand obtained from these methods is used to design the network and coordinate protection relays, but for applications such as load management and energy theft analysis, a higher resolution of power consumption data is required. The cumulative load behavior curve is the sum of individual customers’ load profiles, and the load profile of each individual customer is the sum of the load behavior of its electrical appliances. The methods used to aggregate the behavior of electrical appliances to reach the customer’s load behavior are called “bottom-up” methods [12–15]. The bottom-up approach is recognized as one of the most widely used methods that enables the study of consumer behavioral patterns and the effects of load response programs [16]. These can be achieved by examining the behavioral pattern for using home appliances [17] or by using the data of energy bills together with specific questionnaires [18]. The latter method is based on statistical data that can be very accurate in analyzing buildings energy demand [18]. Some studies have used such accurate information on residents and home appliances to model electricity consumption [19–21] while others have used methods to extract random models that reduce the need for detailed and accurate statistical information [22–26]. A bottom-up approach has been used to model the energy consumption of a home by considering the level of activity of consumers (either when residents are at home or when they are not) and their behavior pattern in [27]. Another model has been developed for studying electricity and hot water consumption based on consumption time data in [20], where a good accuracy of results compared to actual and measured values is demonstrated. Important features of the bottom-up methods are categorized in [28], the most important of which are:

It is simple and easy to implement. • Macroeconomic and social factors can also be included in the model. • It is very suitable for determining the energy consumption and related parameters. • It is always capable of developing, computing and newer studies. • It does not require very detailed information and can be conducted using billing data • and questionnaires.

Therefore, the bottom-up approach is a good way to extract the energy consumption curve as it involves the behavior patterns of residents and the use of diﬀerent appliances [27]. Due to the necessity of knowing the consumption behavior of each individual household, the bottom-up method is used in this study to extract the load proﬁle. Energies 2020, 13, 1287 4 of 24

2.1. Typical Domestic Load Profile Energies 2020, 13, x FOR PEER REVIEW 4 of 24 Household consumption in cold and hot seasons has a completely different behavior pattern in country’smost areas peak of Iran. load The during main reasonthe warm is the season. different In typesorder of to heating better andunderstand cooling systems.the pattern The increaseof load behavior,in the share we of take vapor a closer compression look at the cooling load inconsumed recent years by home has led subscribers. to a significant jump in the country’s peakReference load during [10] the classifies warm season.home elec Intrical order appliances to better understand into four categories: the pattern brown of load goods, behavior, white wegoods, take minora closer appliances, look at the and load lighting consumed systems. by home Relatively subscribers. low consumption electronic equipment such as communicationReference [equipment,10] classifies desktops, home electrical scanners, appliances CD/DVD intoplayers, four TVs, categories: modems brown etc. belong goods, to white the categorygoods, minor of brown appliances, goods. andBasic lighting household systems. necessities Relatively are lowcalled consumption white appliances. electronic These equipment include kitchenware,such as communication laundry and equipment, heating and desktops, cooling scanners,appliances. CD Minor/DVD players,appliances TVs, are modems the type etc. of belongelectrical to equipmentthe category that of brownare typically goods. found Basic householdin any home necessities and are are usually called whiteportable. appliances. Some of These these includeminor applianceskitchenware, include: laundry electric and heatingkettle, toaster, and cooling juicer, appliances. coffee maker, Minor ironing, appliances fan, vacuum are the typecleaner, of electrical sewing machine,equipment mobile that phones, are typically home digital found cameras, in any home radios, and mp3 are players, usually tablets, portable. hair dryer, Some shaver, of these etc. minor appliancesVarious include: factors affect electric the kettle,load profile toaster, of juicer,househol coffd eesubscribers, maker, ironing, the most fan, important vacuum of cleaner, which sewingare: machine, mobile phones, home digital cameras, radios, mp3 players, tablets, hair dryer, shaver, etc. • TemperatureVarious factors in atermsffect theof maximum load profile summer of household temperature subscribers, and minimum the most importantwinter temperature. of which are: • Yearly average temperature. • Temperature in terms of maximum summer temperature and minimum winter temperature. • Economic factors such as the price of all types of energy resources such as electricity, gas, etc., theYearly price average of household temperature. electrical appliances, the per capita income of the household, and the • economicEconomic situation factors such of the as thecommunity. price of all types of energy resources such as electricity, gas, etc., the • • Demographicprice of household factors electrical such as appliances, the number the of per households capita income and of population the household, growth and over the economic a given period.situation of the community. • WelfareDemographic level and factors infrastructure such as the numberlevel of ofhouses. households and population growth over a given period. • Welfare level and infrastructure level of houses. • The modeling performed in this study and the measurement results along with the simulation resultsThe confirm modeling the significant performed effect in this of studysummer and da theytime measurement temperature results on the along load withbehavior the simulation curve. results confirm the significant effect of summer daytime temperature on the load behavior curve. 2.2. Mathematical Modeling of Load Profile 2.2. Mathematical Modeling of Load Profile A prominent feature of the bottom-up model is that it can be used to analyze the load behavior of eachA prominentindividual featuresubscriber. of the Figure bottom-up 1 illustrates model the is thatlogic it used can be for used modeling. to analyze The thedaily load load behavior curve isof actually each individual created by subscriber. repeating Figure two loops.1 illustrates In the thefirst logic loop, used after for choosing modeling. the Thetype daily of household, load curve a loadis actually curve will created be created by repeating for each two of loops. the equipmen In the firstt in loop,the house. after choosingThis procedure the type is ofrepeated household, in the a secondload curve loop will for beall createdthe equipment for each and of the the equipment cumulative in consumption the house. This curve procedure is added is to repeated the previous in the curvessecond to loop obtain for allthe thefinal equipment household and load the curve. cumulative The appliance consumption list varies curve from is added house to to the house, previous so a coefficientcurves to obtainis defined the final as the household level of loadsaturation curve. that The indicates appliance the list likelihood varies from of house a particular to house, home so a beingcoeffi cientequipped is defined with as a theparticular level of saturationappliance that(𝑃 indicates). In fact, the for likelihood a large of number a particular of homes, home being this coefficientequipped withgives a particularthe frequency appliance of a particular (Pstart). In fact,home for appliance. a large number For example, of homes, a thissaturation coefficient level gives of 0.93the frequencyfor an appliance of a particular in 100 home residential appliance. homes For example,means that a saturation there are level 93 ofunits 0.93 forof anthat appliance special equipmentin 100 residential in the 100 homes homes means [13]. that there are 93 units of that special equipment in the 100 homes [13].

Household Start 01 Appliance Start 01

Household Appliance ...... 02 02

Appliance End n Household End m

FigureFigure 1. 1. TheThe bottom-up bottom-up load load modeling modeling diagram. diagram.

Energies 2020, 13, 1287 5 of 24

Assuming that the equipment list and associated saturation range are known, a mathematical model is needed to construct the energy consumption curve. The basic idea is that if a particular appliance is switched on, the power consumption will be added from the time step of switching on to the whole house until the equipment operation cycle is completed and the equipment is switched off. The daily consumption curve will be calculated from the sum of each individual consumption curve when this process is repeated for all appliances. Depending on the customer’s consumption pattern, a specific appliance can be switched on at any time of the day at various times. This part is actually one of the most important parts of modeling. In this study, a start probability function (Pstart) is introduced representing the probability of the appliance turning on at each time step. Any electrical appliance has the highest chance of being turned on at certain times of the day. A clear example of this is the lighting lamps that are most likely to be lit in the early hours of the night, but that does not mean that they do not start at other times. For the mathematical definition of this problem, for each appliance, the probability distribution function is defined whose maximum value or values correspond to peak hours of probability of start, and the starting probability at other times follows a normal distribution pattern. Pstart takes a value between zero and one. When the appliance is off, the search for the next start begins based on Pstart. This is done by generating a random number of probability distributions related to it. When the appliance turns on and completes its duty cycle, the search for the next switch-on time begins. The Pstart probability function can be calculated using the following equation [13]:

Pstart(A, ∆t, h) = P (A, h) f (A, d) Pstep(∆t) Psat(A) (1) hour × × × where Pstart is related to three variables, A indicates the type of the proposed appliance, ∆t is the calculation time step, h is the daily time in hours, and Psat(A) is the saturation level of appliance A as previously described. Phour is the probability factor that specifies the activity level of any appliance at any time of the day. The larger the amount, the higher the probability of the appliance being turned on, and vice versa. f is the frequency of turning the appliance on, which indicates the average number of times a particular appliance is used per day. Pstep is a scaling factor that scales probabilities on the basis of ∆t. Equation (1) applies to all appliances. When an appliance is switched on, its rated power added to the customers’ load profile during the operating cycle, and then the equipment is switched off to begin the search for the next switch on. Standby power of equipment is also considered in this study. For example, refrigerators and TVs consume some power even when they are off, which is included in calculations.

3. Grid-Connected Photovoltaic Source Behavior Small grid connected PV resources have resulted in a significant behavioral change in the load pattern by contributing to supplying part of the customer’s demand and also providing part of the grid’s required power from their surplus. This has made it necessary to consider the impact of these resources in analyzing the customer’s behavior. In this study, the effect of the performance of small photovoltaic sources on the load profile of households is investigated using mathematical modeling and computer simulation. There are various approaches to exploiting solar generation [29]. One of the most common approaches is to generate solar energy through MPPT and to exploit the maximum solar radiation power available. When solar power is operated as MPPT, there will be no freedom to participate in frequency control, because there is no capacity to increase production in this case, however, for the small producers in this study, the main objective is to provide the power consumption and utilize the maximum capacity of the installed system. Therefore, this study investigates a photovoltaic system operated under an MPPT strategy in grid-connected mode and the performance of the proposed system in tracking maximum output power under different sunlight conditions and finally its effect on the load profile of home subscribers is considered. Energies 2020, 13, 1287 6 of 24

3.1. Modeling of Solar Panels The PV module is a non-linear device that can be considered as a current source as shown in Figure2[ 30–32]. Regardless of the internal series resistors, the common current-voltage (I-V) equations of aEnergies solar module2020, 13, x can FOR be PEER expressed REVIEW as in Equation (2); 6 of 24 ! ! qVo Io = NpIg NpIsat exp 1 Irsh (2) 𝐼 =𝑁𝐼 −𝑁𝐼 𝑒𝑥𝑝A KT −1−𝐼 (2) − D mod− − wherewhereIo is 𝐼 the is output the output current current of the of PV the module, PV module,Np is the 𝑁 number is the ofnumber cells in of parallel, cells inI gparallel,is the current 𝐼 is the generatedcurrent bygenerated solar radiation, by solarIsat isradiation, the reverse 𝐼 saturation is the reverse current, saturationq is charge current, of an electron, 𝑞 is chargeVo is theof an outputelectron, voltage 𝑉 ofisPV the module, output AvoltageD is the of ideality PV module, factor of 𝐴 the is diode, the idealityK is the factor Boltzmann’s of the constantdiode, 𝐾 and is the Irsh Boltzmann’sis the current constant due to intrinsic and 𝐼 shunt is the resistance current due of the to intrinsic PV module. shunt resistance of the PV module.

Rs +

Ig D Rsh Vo Ro

Id Ish -

Figure 2. The equivalent circuit of a photovoltaic (PV) module [30]. Figure 2. The equivalent circuit of a photovoltaic (PV) module [30].

The saturation current of the solar module Isat varies with temperature ﬂuctuations as formulated 𝐼 in EquationThe (3):saturation current of the solar module varies with temperature fluctuations as formulated in Equation (3): 3 !! Tmod qEg 1 1 Isat = Ior exp (3) T KT T T r 𝑇 mod 𝑞𝐸r − mod1 1 𝐼 =𝐼 𝑒𝑥𝑝 − (3) S𝑇i 𝐾𝑇 𝑇 𝑇 Ig = Isc + It(T Tr) (4) 1000 mod − 𝑆 where Ior is the saturation current at reference𝐼 =𝐼 temperature+𝐼𝑇 (Tr),−𝑇Eg is the band-gap energy, It is the (4) 1000 short-circuit current temperature coeﬃcient, Isc is the short-circuit current of PV module, Si is the solar insolation,where 𝐼 and isT modthe issaturation temperature current of the at PVreference module temperature in K. (𝑇), 𝐸 is the band-gap energy, 𝐼 is theThe short-circuit current through current the temperature shunt resistance coefficient, is calculated 𝐼 is asthe follows: short-circuit current of PV module, 𝑆 is the solar insolation, and 𝑇 is temperature of the PV module in K. Vo The current through the shunt resistIancersh = is calculated as follows: (5) NsRsh 𝑉 𝐼 = (5) where Ns Is the number of cells in series, and Rsh is the internal𝑁𝑅 shunt resistance of the PV module.

3.2.where Maximum 𝑁 Is Power the Pointnumber Tracking of cells (MPPT) in series, Modeling and 𝑅 is the internal shunt resistance of the PV module. Several algorithms have been proposed for maximum power point tracking. These algorithms can3.2. be dividedMaximum into Power three Point general Tracking categories (MPPT) [33 Modeling,34]: Perturb and observation (P&O) algorithm [35–37]; • Several algorithms have been proposed for maximum power point tracking. These algorithms Incremental conductance algorithm [37–39]; • can be divided into three general categories [33,34]: Soft computing methods such as fuzzy logic control-based algorithms [40], artiﬁcial neural network • • Perturb and observation (P&O) algorithm [35–37]; (ANN)-based algorithms [41], Genetic Algorithm (GA)-based algorithms [42], Particle Swarm • Incremental conductance algorithm [37–39]; Optimization (PSO) [43], etc. • Soft computing methods such as fuzzy logic control-based algorithms [40], artificial neural Anynetwork of the mentioned (ANN)-based algorithms algorithms could [41], be Genetic adapted Al forgorithm the purpose (GA)-based of this algorithms research due [42], to Particle the ﬂexibilitySwarm of ANN-based Optimization model (PSO) used. [43], The etc. incremental conductance method [38,39] is used to model the maximum power point tracking in this study. The dP/dV must be equal to zero at the maximum Any of the mentioned algorithms could be adapted for the purpose of this research due to the power point [44], so: flexibility of ANN-basedd( modelV I) used.dV The incrementaldI conductancedI method [38,39] is used to model × = I + V = I + V = 0 (6) the maximum power pointdV trackingdV in ×this study.dV × The dP/dVdV must× be equal to zero at the maximum power point [44], so: 𝑑𝑉×𝐼 𝑑𝑉 𝑑𝐼 𝑑𝐼 = ×𝐼+ ×𝑉=𝐼+ ×𝑉=0 (6) 𝑑𝑉 𝑑𝑉 𝑑𝑉 𝑑𝑉

𝑑𝐼 𝐼 + =0 (7) 𝑑𝑉 𝑉

Energies 2020, 13, 1287 7 of 24

dI I Energies 2020, 13, x FOR PEER REVIEW + = 07 of (7) 24 dV V AtAt any any given given moment, moment, the the MPPT MPPT checks chec theks zero-sum the zero-sum requirement requirement of dI/dV ofand dI/dVI/V. Ifand the I/V resultant. If the isresultant not zero, is the not proportional-integral zero, the proportional-integral (PI) controller (PI) considerscontroller theconsiders value ofthe the value product of the as product error and as minimizeserror and minimizes it. The value it. atThe the value output at ofthe the output PI controller of the PI is controller the amount is the of change amount required of change in therequired duty cycle.in the This duty value cycle. is This added value to the is currentadded to duty the cycle current value. duty For cycle better value. convergence, For better the convergence, initial value the of dutyinitial cycle value has of been duty set cycle to 0.75 has by been trial andset to error. 0.75 The by concepttrial and of error. the proposed The concept controller of the is shownproposed in Figurecontroller3. is shown in Figure 3.

Vpv/Ipv

+ Vref/Iref d MPPT Algorithm PI -

FigureFigure 3. 3.Block Block diagramdiagram ofof maximummaximum powerpower pointpoint trackingtracking (MPPT) (MPPT) model. model. 4. Data Mining Methods for Fraud Detection 4. Data Mining Methods for Fraud Detection Detection of anomalies is done using the famous knowledge discovery model. These models are Detection of anomalies is done using the famous knowledge discovery model. These models widely used in data-mining research [2,45–47]. Given the similarity of energy consumption behavior in are widely used in data-mining research [2,45–47]. Given the similarity of energy consumption small areas with relatively homogeneous distribution and living standards, the use of non-supervised behavior in small areas with relatively homogeneous distribution and living standards, the use of knowledge discovery methods allows data clustering. The SOM method is used for clustering and non-supervised knowledge discovery methods allows data clustering. The SOM method is used for then detecting anomalies in subscriber consumption profile in this study. Anomalies in the load profile clustering and then detecting anomalies in subscriber consumption profile in this study. Anomalies can be the result of a common fraud or a failure in the metering system, which in any case is the in the load profile can be the result of a common fraud or a failure in the metering system, which in non-monetization of the relevant shared energy consumption for distribution companies, equivalent to any case is the non-monetization of the relevant shared energy consumption for distribution non-technical losses. companies, equivalent to non-technical losses. The SOM network uses competitive learning to train and is developed based on specific The SOM network uses competitive learning to train and is developed based on specific characteristics of the human brain. The cells in the human brain are organized in different areas so that characteristics of the human brain. The cells in the human brain are organized in different areas so in different sensory areas they are presented with meaningful computational maps. Self-organized that in different sensory areas they are presented with meaningful computational maps. networks are structurally divided into several categories in which we used the Kohonen network in Self-organized networks are structurally divided into several categories in which we used the this study. The SOM is an unsupervised neural network composed of neural neurons in a regular, Kohonen network in this study. The SOM is an unsupervised neural network composed of neural low-dimensional grid structure. Each neuron has an n-dimensional weight vector where n is the neurons in a regular, low-dimensional grid structure. Each neuron has an n-dimensional weight dimension of the input vectors. Weight vectors (synapses) attach the input layer to the output layer. vector where n is the dimension of the input vectors. Weight vectors (synapses) attach the input This is called the output layer, map or competitive layer. The neurons are connected by a neighborhood layer to the output layer. This is called the output layer, map or competitive layer. The neurons are function (as shown in Figure4). Each input vector, by most similarity, activates a neuron in the output connected by a neighborhood function (as shown in Figure 4). Each input vector, by most layer called the winning cell. The similarity is usually measured by the Euclidean distance between similarity, activates a neuron in the output layer called the winning cell. The similarity is usually two vectors [48]. measured by the Euclidean distance between two vectors [48]. Xn h i2 Dj = Wi,j Xi (8) − = 𝐷 =𝑊i 1 , −𝑋 (8) where Xi is the ith input vector of the neural network, Wi,j is the the weight vector which connects the ithwhere input 𝑋 to theis the jth output,ith input and vectorDj is the of sumthe ofneural the Euclidean network, distance 𝑊, is between the the input weight sample vectorXi andwhich its associatedconnects the weight ith input vector to to the output jth output,j called and a map 𝐷 isunit. the sum of the Euclidean distance between input sample 𝑋 and its associated weight vector to output j called a map unit.

Energies 2020, 13, 1287 8 of 24 Energies 2020, 13, x FOR PEER REVIEW 8 of 24

Figure 4. The structure of self-organized neural network (SOM) network. Figure 4. The structure of self-organized neural network (SOM) network. The most important difference between the SOM training algorithm and other vector quantization algorithmsThe is thatmost in important addition to thedifference highest matchingbetween unitthe weightSOM training (the winner algorithm neuron), and the weightsother vector of the neighboringquantization cellsalgorithms of the winningis that in celladdition are also to updated.the highest Close-up matching observations unit weight in (the the winner input spaceneuron), activatethe weights two close-up of the unitsneighboring in the map. cells Theof the training winning phase cellcontinues are also updated. until the Cl weightose-up vectors observations reach in steadythe stateinput and space no longeractivate change: two close-up units in the map. The training phase continues until the weight vectors reach steady state and no longer change: new = old + old Wi,j Wi,j hi,j Xi Wi,j (9) 𝑊, =𝑊, +ℎ,−𝑋 −𝑊, (9) new old wherewhereWi, j𝑊,is the is the updated updated weight weight vector vector between between input input cell celli and i and output output cell cellj, Wj, i, j𝑊,is theis the previousprevious weight weight vector vector between between input input vector vectorX i 𝑋and and weight weight vector vector to to output output neuron neuronj ,j, andand hℎi,,j is is thethe neighboring neighboring function. function. AfterAfter the trainingthe training phase, phase, i.e., i.e., in the in mappingthe mapping phase, phase, it will it will be possible be possible to automatically to automatically classify classify each each inputinput data data vector. vector. In the In trainingthe training phase, phase, auxiliary auxiliary tags ta suchgs such as shared as shared zip codezip code (specifying (specify geographicaling geographical areaarea and and living living standard), standard), main main fuse fuse capacity capacity of of meter, meter, type type of of meter meter (digital(digital oror analog),analog), tariff tariff typetype and andmeter meter reading reading period (time(time tag)tag) areare used. used. The The anomaly anomaly detection detection algorithm algorithm in electricalin electrical energy energy consumptionconsumption is illustratedis illustrated in Figurein Figure5. The 5. procedureThe proced forure detectingfor detecting abnormalities abnormalities in a in customer’s a customer’s behaviorbehavior is such is such that that a mass-normal a mass-normal behavioral behavioral dataset dataset is generatedis generated by by simulation. simulation. This This data data is is used used as as thethe input inputdata dataof of a a SOM SOM network networkfor for neural neural networknetwork training,training, andand afterafter clusteringclustering the bulk data, the thecenters of of each each cluster cluster are are considered considered as as the the norm normalal behavior behavior center. center. Among Among the theconsumption consumption profiles profileslocated located in each in eachcluster, cluster, profiles profiles whose whose elements elements have havethe maximum the maximum Euclidean Euclidean distance distance to the to center the of centerthe of respective the respective cluster cluster are considered are considered as normal as normal boundary boundary load loadprofiles profiles and andcustomers customers located located outside outsidethis boundary this boundary are classified are classified as suspected as suspected substrates substrates.. The Euclidean The Euclidean distance distance of the suspected of the suspected subscribers subscribersto the anomaly to the anomalyis normalized is normalized based on 9 based and the on norm 9 andalized the normalized distance of distanceany suspected of any subscriber suspected from subscriberthe nearest from center the nearest of the cluster center is of defined the cluster as the is “anomaly defined as index”. the “anomaly index”. The procedure for detecting anomalies in customers’ behavior is such that a mass data of normal behavior is generated by simulation. This data is used as the input data of a SOM network for neural network training, and after clustering the bulk data, the centers of each cluster are considered as the normal behavior centers. The load curve of each customer lies at a specified distance from the centers of the clusters. The distance of each load curve from the center of the corresponding cluster is calculated using Equation (10): ⎛ ⎞ 𝐷, = 𝑃, −𝑃, (10) ⎝ ⎠ 𝐷 where , is the distance of the ith load curve from the center of the jth cluster. t is the time, 𝑃, is

the load of the ith customer at time t, 𝑃, is the load of the center of the jth cluster at time t, and 𝑛 is the number of clusters. The membership function of each load curve in any cluster is calculated as below:

Energies 2020, 13, x FOR PEER REVIEW 9 of 24

1 Energies 2020, 13, 1287 𝜇, =𝑚𝑎𝑥 (11) 9 of 24 𝐷,

where 𝜇, is the membership of any customers to normal behavior.

Start

Generate Load Profiles for Customers with no PV

Mass Data Generate Load Profiles Generation for Customers with grid-connected PV

Integrate all generated data

Clustering consumption profiles and determining normal profile centers

Get test customer data

Is the customers’ load profile This customer included in any of the normal Y Fraud Test behaves normally behavior clusters

This customer is suspected

Inspection

End

Figure 5. Flowchart of proposed method for fraud detection in power distribution networks. Figure 5. Flowchart of proposed method for fraud detection in power distribution networks. 5. Case Study The procedure for detecting anomalies in customers’ behavior is such that a mass data of normal behavior5.1. Simulation is generated of the Load by simulation.Profile of Household This dataCustomers is used as the input data of a SOM network for neural network training, and after clustering the bulk data, the centers of each cluster are considered as the normal behavior centers. The load curve of each customer lies at a speciﬁed distance from the centers of the clusters. The distance of each load curve from the center of the corresponding cluster is calculated using Equation (10):  tuv nc  24   X 2 D =  PL P  (10) Li,j  i,t − Cj,t   =  t 1 j=1 Energies 2020, 13, 1287 10 of 24

where DLi,j is the distance of the ith load curve from the center of the jth cluster. t is the time, PLi,t is the load of the ith customer at time t, PCj,t is the load of the center of the jth cluster at time t, and nc is the number of clusters. The membership function of each load curve in any cluster is calculated as below: ! Energies 2020, 13, x FOR PEER REVIEW 1 10 of 24 µi,j = max (11) Characteristics of electrical consumer appliancesD Liof ,ja total of 76 residential houses were collected using a questionnaire in Golgouah, Mazandaran, Iran. All meters of these customers were tested and evaluated prior to the measurements. All of these subscribers are powered by a 20/0.4 where µi,j is the membershipkV-160 kVA pole-mounted of any substation. customers A TDL104 to normal data logger behavior. was used to measure these customers’ consumption and extract the load behavior curve. In 30 min time intervals, the information of the instantaneous active power, the instantaneous reactive power, the instantaneous voltage and the 5. Case Study average consumed energy were measured for a total of 82 customers [49]. The results obtained in the measurement are used to validate the proposed model. In order to obtain homogeneous and analytic 5.1. Simulation of theinformation, Load Proﬁleit has been of attempted Household to perform Customers measurements on feeders with similar welfare levels. For this purpose, a three-dimensional map of the load density of domestic loads was implemented in the geographic information system (GIS) for the city of Galougah (Figure 6) [50]. The specifications of the Characteristicsfeeder of measured electrical are given consumer in Table 1. appliances of a total of 76 residential houses were collected using a questionnaire in Golgouah, Mazandaran, Iran. All meters of these customers were tested and Table 1. Specifications of the data logger installation point. evaluated prior to the measurements. All of these subscribers are powered by a 20/0.4 kV-160 kVA Transformer Customer Classes pole-mounted substation.Substation AName TDL104 Nominal data logger was used to measureCommercial these customers’ and consumption Domestic Public Industrial and extract the load behavior curve.Capacity In (kVA) 30 min time intervals, the informationOther of the instantaneous Zeytoon Complex 160 76 2 - 4 active power, the instantaneous reactive power, the instantaneous voltage and the average consumed energy were measuredBased for on athe total data obtained of 82 customersfrom the question [49naires,]. The home results appliance obtained brands of the in Iranian the measurement are market and the energy label class of appliances, the list of home appliances used was extracted as used to validate thedescribed proposed in Table model.2. The pattern In used order in this to sectio obtainn is adapted homogeneous from [13]. Equation and (1) analytic is applied to information, it has been attempted toany perform of the electrical measurements energy-consuming onappliances feeders. At the with beginning similar of each welfare computational levels. step, a For this purpose, random number between 0 and 1 is generated and compared with 𝑃. If 𝑃 is greater than a three-dimensionalthe random map number of the generated, load density the consum ofer domesticswitches on and loads remains was on until implemented 𝑡=𝑡 +𝑡.in the geographic After that, the process of checking the condition for the next switch-on begins again. If the information systemappliance (GIS) also for has a the certain city power of consumption Galougah in standby (Figure mode,6)[ its standby50]. Thepower speciﬁcationsis added to the of the feeder measured are givenentire in power Table consumption1. curve as a constant. This holds true for loads such as televisions. The value of 𝑡 is the average time period each appliance stays on [13].

Figure 6. Domestic load density of Galougah [50]. Figure 6. Domestic load density of Galougah [50]. The consumed energy by each home during the one-month period can be calculated using Equation Table(12). Equation 1. Speciﬁcations (12) gives the required of the va datalues for logger verifying installation the proposed point.model in electric power distribution networks with no smart energy metering systems. Transformer Nominal3600 × 𝑃 + 𝑓 ∑ 𝑃 ×𝑡 ×30Customer Classes (12) Substation Name 𝐸 = kWh/month Capacity (kVA) Domestic3.6 × 10 Public Industrial Commercial and Other Zeytoon Complex 160 76 2 - 4

Based on the data obtained from the questionnaires, home appliance brands of the Iranian market and the energy label class of appliances, the list of home appliances used was extracted as described in Table2. The pattern used in this section is adapted from [ 13]. Equation (1) is applied to any of the electrical energy-consuming appliances. At the beginning of each computational step, a random number between 0 and 1 is generated and compared with Pstart. If Pstart is greater than the random number generated, the consumer switches on and remains on until t = tstart + tcycle. After that, the process of checking the condition for the next switch-on begins again. If the appliance also has a certain power consumption in standby mode, its standby power is added to the entire power consumption curve as a constant. This holds true for loads such as televisions. The value of tcycle is the average time period each appliance stays on [13]. Energies 2020, 13, 1287 11 of 24

Table 2. Power consumption characteristics of household electrical appliances.

Mean Daily Appliance Nominal Time Per Cycle Appliance Standby [W] Starting Saturation Wattage [W] [min] Frequency [f] Microwave Oven 0.2 1500 - 5 2 Refrigerator 1 180 10 44.5 15 Coﬀee Maker 0.1 1200 - 0.76 6 Clothes Washer 0.75 2000 - 0.22 65 Other Kitchen Appliance 0.2 300 - 0.1 10 TV 1 180 10 2 120 PC and Laptop 0.92 110 3 2.5 70 Gaming Tools 0.22 100 2 1 120 Air Conditioner 0.9 2100 - 2 120 Hair Dryer 1 1200 - 0.2 7 Lighting 1 160 - 10 30 Electric Kettle 0.4 480 - 2 6 Dish Washer 0.15 2000 - 0.14 190 Iron 1 1700 - 0.3 7 Cooling and Ventilation fans 0.91 80 - 1 120 Battery Chargers and Voltage Adaptors 1 5 - 3 60 Electric Water Heating 0 2000 - - -

The consumed energy by each home during the one-month period can be calculated using Equation (12). Equation (12) gives the required values for verifying the proposed model in electric power distribution networks with no smart energy metering systems.

h Pnapp i 3600 P + f Pnom t 30 × standby n=1 × cycle × Emonthly = kWh/month (12) 3.6 106 × where Pstandby is the standby power of each appliance (W), Pnom is the nominal power of each appliance (W), napp is the number of appliances in each home, and tcycle is the the average time period that each appliance stays on. Mathematical simulation is performed using MATLAB. The simulation is done for one day and is extended to thirty days. The behavior of loads such as refrigerators and cooling systems largely depends on the behavior of homeowners, but the modeling of this problem will be very complex. For simplification, the average single-cycle behavior of these types of equipment is used to simulate. Simulations and measurements are related to the warm season of the year. Subscriber well-being is another issue that has a profound effect on subscriber behavior. This study uses data from subscribers with approximately equal welfare levels. Baseline information of Table2 is used for the simulations. This data arrangement, adapted from [13], has been modified to fit the home appliance available in the Iranian market [51]. The table also includes a column called saturation level, which is the ratio of the number of household appliances of each type to the total number of dwellings under study. The switch-on likelihood of each of the appliances listed in Table2 varies at di fferent times of the day. For example, it is clear that the switch-on probability of the cooling system are highest in the hot hours of the day. Also, lighting loads are more likely to happen at night. Values less than 1 for the start frequency in Table2 mean that the appliance is switched on once in a few days. For example, the value of 0.22 for the washing machine indicates that this equipment is mostly turned on once every four to five days and does not function daily. Pstart is the probability of each equipment turning on at any given time step. In this study, unlike similar studies, the start-on probability distribution function of each device is used instead of using a constant start-on program [52] or using a specified Pstart value as the start-up probability of each device on every hour [13,19]. The starting probability distribution function of each appliance is assumed to be normal around the maximum possible start hours. Figure7 shows the start-on probability density of each of the equipment listed in Table2. Equipment such as air coolers are more likely to start during hot hours, but in the case of refrigerators, no hours predominate over other hours, as seen. Energies 2020, 13, 1287 12 of 24 Energies 2020, 13, x FOR PEER REVIEW 12 of 24

(a) Microwave Oven (b) Refrigerator (c) Coffee Maker

(d) Clothes Washing Machine (e) Regular Kitchen Appliances (f) TV

(g) Laptops and PCs (h) Gaming Tools (i) Cooling

(j)Hair Drying (k) Lighting (l)Electric Kettle

(m) Dish Washer (n) Clothes Ironing (o) Cooling and Ventilation fans

Figure 7. Cont.

Energies 2020, 13, x FOR PEER REVIEW 13 of 24

Energies 2020, 13, 1287 13 of 24 Energies 2020, 13, x FOR PEER REVIEW 13 of 24

(p) Battery Chargers and Voltage Adaptors

Figure 7. The start-on probability distribution of home appliances. (a) Microwave Oven; (b) Refrigerator; (c) Coffee Maker;(p) Battery (d Chargers) Clothes and Washing Voltage Machine;Adaptors (e) Regular Kitchen Appliances; (f) TV; (g) Laptops and PCs; (h) Gaming Tools; (i) Cooling; (j) Hair Drying; (k) Lighting; (l) Electric FigureFigure 7. 7. The start-onstart-on probability probability distribution distribution of home of home appliances. appliances. (a) Microwave (a) Microwave Oven; (b) Refrigerator;Oven; (b) Kettle; (m) Dish Washer; (n) Clothes Ironing; (o) Cooling and Ventilation fans; (p) Battery Chargers Refrigerator;(c) Coﬀee Maker; (c) Coffee (d) Clothes Maker; Washing (d) Clothes Machine; Washing (e) Regular Machine; Kitchen (e) Appliances;Regular Kitchen (f) TV; Appliances; (g) Laptops ( andf) and Voltage Adaptors. TV;PCs; (g) ( hLaptops) Gaming and Tools; PCs; (i )(h Cooling;) Gaming (j) Tools; Hair Drying; (i) Cooling; (k) Lighting; (j) Hair (lDrying;) Electric (k Kettle;) Lighting; (m) Dish (l) Electric Washer; Kettle; (m) Dish Washer; (n) Clothes Ironing; (o) Cooling and Ventilation fans; (p) Battery Chargers (nThe) Clothes simulation Ironing; (usingo) Cooling the andproposed Ventilation model fans; genera (p) Batterytes the Chargers behavioral and Voltage curve Adaptors. of each electrical and Voltage Adaptors. appliance. The total load curve of each house is obtained by integrating the load behavior curves of The simulation using the proposed model generates the behavioral curve of each electrical the electrical equipment inside it. Figure 8 shows the load behavior of several household customers appliance.The simulation The total using load curvethe proposed of each house model is obtainedgeneratesby the integrating behavioral the curve load behaviorof each electrical curves of with different load behavior types. The horizontal axis in the diagrams is calibrated in minutes. appliance.the electrical The equipmenttotal load curve inside of it. each Figure house8 shows is ob thetained load by behavior integrating of several the load household behavior customerscurves of thewith electrical diﬀerent equipment load behavior inside types. it. Figure The horizontal8 shows the axis load in thebehavior diagrams of several is calibrated household in minutes. customers with different load behavior types. The horizontal axis in the diagrams is calibrated in minutes. 5000 2500 4000 2000 3000 1500 50002000 25001000 40001000 2000500 3000 0 1500 0 1

2000 1 Load Power (W)

1000Load Power (W) 121 241 361 481 601 721 841 961 121 241 361 481 601 721 841 961 1000 1081 1201 1321

500 1081 1201 1321 0 0 1

time (mins) 1 time (mins) Load Power (W) Load Power (W)

121 241 361 481 601 721 841 961 121 241 361 481 601 721 841 961 1081 1201 1321 (a) (b) 1081 1201 1321 time (mins) time (mins)

3000 (a) 5000 (b) 2500 4000 2000 3000 1500 3000 50002000 25001000 40001000 2000500 3000 1500 0 0 1 1 Load Power (W) 1000 2000Load Power (W) 132 263 394 525 656 787 918 121 241 361 481 601 721 841 961 1049 1180 1311 500 1081 1201 1321 1000 0 0 1 1 Load Power (W) time (mins) Load Power (W) time (mins) 132 263 394 525 656 787 918

121 241 361 481 601 721 841 961 1049 1180 1311 1081 1201 1321 (c) (d) time (mins) time (mins) Figure 8. (a)–(d) Simulation result: load profiles of four common samples with four different load profile types. (c) (d) Figure 8. (a)–(d) Simulation result: load profiles of four common samples with four different load 5.2. Model Validation profile types. Figure9 illustrates the comparison between simulation results and measurement results in the Figure 8. (a)–(d) Simulation result: load profiles of four common samples with four different load sample5.2. Model grid Validation with the specifications given in Table1 to validate the model. Measurement results belong profile types. to the mean days of 16 July to 10 August 2019 [53]. Due to the different behavior of subscribers on Figure 9 illustrates the comparison between simulation results and measurement results in the holidays and semi-holidays, weekends are omitted on average load behavior calculations. Simulation 5.2.sample Model Validationgrid with the specifications given in Table 1 to validate the model. Measurement results results are obtained with one-minute accuracy, but they need to be calculated in the form of 30 min belong to the mean days of 16 July to 10 August 2019 [53]. Due to the different behavior of sets,Figure since the9 illustrates measurements the comparison were made between in 30 min simulation intervals. results and measurement results in the sample grid with the specifications given in Table 1 to validate the model. Measurement results belong to the mean days of 16 July to 10 August 2019 [53]. Due to the different behavior of

Energies 2020, 13, x FOR PEER REVIEW 14 of 24

subscribers on holidays and semi-holidays, weekends are omitted on average load behavior Energiescalculations.2020, 13, 1287Simulation results are obtained with one-minute accuracy, but they need 14to of 24be calculated in the form of 30 min sets, since the measurements were made in 30 min intervals.

90 80 70 60 50 40 Measurement 30 Simulation 20 10

Total Load of 82 Customers [kW] 0 0:00 3:00 6:00 9:00 12:00 15:00 18:00 21:00 0:00 Time [hr]

FigureFigure 9.9. ComparisonComparison ofof loadload proﬁleprofile measurementmeasurement resultsresults andand simulationsimulation results.results.

ToTo calculate calculate the the amount amount of of error error between between the the simulation simulation results results and and the the measurement measurement results, results, the valuesthe values of normalized of normalized root mean root squaremean errorsquare (RMSE errornorm (𝑅𝑀𝑆𝐸), normalized), normalized mean absolute mean error absolute (MAE errornorm) and(𝑀𝐴𝐸 relative) and mean relative error (meanMRE) error are calculated (𝑀𝑅𝐸) are as calculated follows [ 54as]: follows [54]:

v 𝑅𝑀𝑆𝐸 = tu ∑y 𝑒 −𝑚 (13) X  1 1  2 RMSEnorm =  (ei mi)  (13) avg(mi) y −  i=1 1 𝑀𝐴𝐸 = y|𝑒 −𝑚| (14) 𝑦 × 𝑎𝑣𝑔𝑚X 1 MAEnorm = ei mi (14) y avg(mi) | − | × i=1 1 𝑒 −𝑚 𝑀𝑅𝐸 = y (15) 1 X ei mi 𝑦 𝑚 MRE = − (15) y mi i=1 where 𝑒 and 𝑚 are the values obtained from the simulation and the measured values e m whererespectively.and Alsoare the𝑦 represents values obtained the number from of the values simulation to be compared. and the measured values respectively. Also y represents the number of values to be compared. The calculated values of 𝑅𝑀𝑆𝐸 , 𝑀𝐴𝐸 , and 𝑀𝑅𝐸 are 8.89%, 6.19% and 7.42%, RMSE MAE MRE respectively.The calculated The average values of magnitudenorm , of thenorm absolu, andte valuesare 8.89%,of simulation 6.19% and errors 7.42%, is respectively.4.69%. The Theaverage average daily magnitude energy consumption of the absolute measured values is 13 of.51 simulation kWh per errorscustomer is4.69%. compared The to average 13.03 kWh daily as energythe average consumption daily energy measured consumption is 13.51 per kWh customer per customer obtained compared from the to simulation, 13.03 kWh aswhich the averageshows a dailydifference energy of consumptionapproximately per 3.5%. customer obtained from the simulation, which shows a difference of approximately 3.5%. 5.3. Simulation of the Effect of Grid-Connected Photovoltaic Resources 5.3. Simulation of the Effect of Grid-Connected Photovoltaic Resources It is assumed that 10% of subscribers will use grid-connected photovoltaic panels to supply It is assumed that 10% of subscribers will use grid-connected photovoltaic panels to supply their their required energy and sell their surplus energy to the global grid. Considering the average floor required energy and sell their surplus energy to the global grid. Considering the average floor area area of homes of the studied town and the on-grid inverter panels and inverters available in the of homes of the studied town and the on-grid inverter panels and inverters available in the market, market, the rated power of 1, 1.5 and 2 kW grid PV systems is considered. The characteristics of the the rated power of 1, 1.5 and 2 kW grid PV systems is considered. The characteristics of the simulated simulated modules in this study are described in Table 3. The specifications given in Table 3 are modules in this study are described in Table3. The specifications given in Table3 are specific to specific to standard temperature conditions (25 °C) and the increase in temperature reduces the standard temperature conditions (25 C) and the increase in temperature reduces the efficiency of efficiency of the photovoltaic module◦ [55,56]. The effect of temperature on the output power of the the photovoltaic module [55,56]. The effect of temperature on the output power of the PV module is PV module is modeled by coefficients µIsc and µVoc. The performance factor (PR) depends on a modeled by coefficients µIsc and µVoc. The performance factor (PR) depends on a number of factors, number of factors, including inverter losses, AC and DC cable losses, shadow or cloud output including inverter losses, AC and DC cable losses, shadow or cloud output power loss, and reduced power loss, and reduced efficiency caused by dust and snow on the modules. efficiency caused by dust and snow on the modules.

Energies 2020, 13, 1287 15 of 24

Energies 2020, 13, x FOR PEER REVIEW 15 of 24 Table 3. Specifications of the simulated PV module. Table 3. Specifications of the simulated PV module. Temperature Nominal MaximumMaximum Power Temperature Coefficient Size [mm Efficiency Performance NominalPower Technology Performan Power Coefficient Sizemm] [mm× × Efficiency[%] Ratio [PR] Power[W] Technology Impp Vmpp µIsc µVoc ce Ratio [A]Impp Vmpp[V] [mAµIsc/ C] [mVµVoc/ C] mm] [%] [W] ◦ ◦ [PR] 250 Si-poly 8.330[A] 30.0[V] [mA/°C] 4.3 [mV/°C]137 1640 992 15.3 0.5 0.9 − × − 250 Si-poly 8.330 30.0 4.3 −137 1640 × 992 15.3 0.5−0.9 The temperature profile and the amount of solar radiation power are other required data. The temperature profile and the amount of solar radiation power are other required data. These These data are available with a maximum resolution of 1 h (Figures 10 and 11). As shown in Figure 10, data are available with a maximum resolution of 1 h (Figures 10 and 11). As shown in Figure 10, the the solar radiation power in the study period is very diffuse and variable. The reason for this is the solar radiation power in the study period is very diffuse and variable. The reason for this is the proximity of the city under study to the Caspian Sea and, as a result, high cloud changes. The effect of proximity of the city under study to the Caspian Sea and, as a result, high cloud changes. The effect of these drastic changes is modeled with the help of the performance factor (PR). In this study, the PR value these drastic changes is modeled with the help of the performance factor (PR). In this study, the PR is assumed to follow a normal probability distribution in the range of the numbers given in Table3. value is assumed to follow a normal probability distribution in the range of the numbers given in Table The load profile of a sample customer with a PV module is shown in Figure 12. The photovoltaic panel 3. The load profile of a sample customer with a PV module is shown in Figure 12. The photovoltaic connected to this particular customer is intended as 1 kW. At certain times, the customer load profile panel connected to this particular customer is intended as 1 kW. At certain times, the customer load goes negative. This is due to the times when the amount of power generated by the PV exceeds the profile goes negative. This is due to the times when the amount of power generated by the PV exceeds load consumed and the customer delivers surplus power to the grid. the load consumed and the customer delivers surplus power to the grid.

40 16-Jul 17-Jul 35 18-Jul C]

o 19-Jul 30 20-Jul 21-Jul 25 22-Jul Temperature[ 23-Jul 20 24-Jul 25-Jul 15 26-Jul 0:00 3:00 6:00 9:00 12:00 15:00 18:00 21:00 0:00 27-Jul Time [hr]

FigureFigure 10. 10.Temperature Temperature proﬁles profiles for for the the study study days. days.

Energies 2020, 13, 1287 16 of 24

Energies 2020, 13, x FOR PEER REVIEW 16 of 24

600 16-Jul 17-Jul 500 18-Jul 19-Jul 400 20-Jul 21-Jul 300 22-Jul 23-Jul

200 24-Jul

Solar Irradiation [W/m2] 25-Jul 26-Jul 100 27-Jul 28-Jul 0 29-Jul 21:00 0:00 3:00 6:00 9:00 12:00 15:00 18:00 21:00 0:00 3:00 30-Jul Time [hr]

Figure 11. The amount of sunlight radiation during the days under study. Energies 2020, 13, x FORFigure PEER 11. REVIEWThe amount of sunlight radiation during the days under study. 17 of 24

Customers equipped with a grid-connected PV are connected to the grid in two ways; one is a 2500 customer whose photovoltaic panels are connected directly to the grid via the inverter and then the energy meter. All the solar energy generated by these customers is sold to the grid in the retail 2000 market. These customers purchase all their needed electricity from the global network. This type of connection is used1500 in cases where the energy generated by the customer is purchased from the customer at a price higher than the energy sales tariffs, in order to encourage the development of renewable energy 1000production. Obviously, these customers fall into the category of subscribers without PV in terms of load behavior analysis. The second category is customers who self-supply by PV power and deliver500 surplus electricity to the grid. In the analysis performed in this study, Load Power [W] these customers, which are connected to the global network by means of bi-directional meters, fall into the clusters of PV-equipped0 subscribers. In fact, the load profile of these subscribers is the result of subtracting the 0:00consum 1:59ption 4:00 and 6:00 the 7:59 production 10:0012:0013:5916:0018:0019:5922:00 power. Iran’s National-500 Smart Metering Program, known as FAMAM, collects the metering data every Time [hr] 15 min. Although simulation results are available with a resolution of one minute, the simulations of the load behavior are appropriately adapted for 15 min intervals. FigureFigure 12. 12. LoadLoad profile proﬁle of of a a sample sample customer customer with with grid-connected PV.

5.4. MassCustomers Data Generation equipped with a grid-connected PV are connected to the grid in two ways; one is a customer whose photovoltaic panels are connected directly to the grid via the inverter and then the In order to better train the neural network used in the analysis, 5000 load profiles were energy meter. All the solar energy generated by these customers is sold to the grid in the retail market. generated using the proposed models and simulation. Ten percent of these subscribers receive part These customers purchase all their needed electricity from the global network. This type of connection of their energy from rooftop photovoltaic panels and sell surplus generation power to the grid is used in cases where the energy generated by the customer is purchased from the customer at a through the retail market. Using the initial mass data generated from simulation to train the SOM price higher than the energy sales tariﬀs, in order to encourage the development of renewable energy neural network does not lead to an analyzable result. One of the reasons is the high number of production. Obviously, these customers fall into the category of subscribers without PV in terms of elements of the input matrix. Clustering of 15 min load curves has little convergence in addition to theload high behavior computational analysis. Thecost. second On the category other hand, is customers since the whocurves self-supply of the solar by radiation PV power are and available deliver onsurplus an hourly electricity average, to the virtually grid. Ina 15 the min analysis load curve performed analysis in will this not study, have these a significant customers, effect which on the are accuracyconnected of to the the globalsimulation. network By byclustering means of the bi-directional mass-produced meters, curves, fall into the the load clusters behavior of PV-equipped curves of non-PV customers fall into 22 clusters and the PV-connected load profiles fall into 26 clusters with different characteristics as shown in Figure 13.

Figure 13. All cluster centers of mass data.

5.5. Fraud Detection The anomalies of power distribution networks fall into five categories: 1. Malfunctioning meters.

Energies 2020, 13, x FOR PEER REVIEW 17 of 24

2500

2000

1500

1000

500 Load Power [W] Energies 2020, 13, 1287 17 of 24 0 0:00 1:59 4:00 6:00 7:59 10:0012:0013:5916:0018:0019:5922:00 subscribers. In fact, the-500 load profile of these subscribers is the result of subtracting the consumption and the production power. Time [hr] Iran’s National Smart Metering Program, known as FAMAM, collects the metering data every 15 min. Although simulationFigure 12. Load results profile are of available a sample withcustomer a resolution with grid-connected of one minute, PV. the simulations of the load behavior are appropriately adapted for 15 min intervals. 5.4. Mass Data Generation 5.4. Mass Data Generation In order to better train the neural network used in the analysis, 5000 load profiles were generatedIn order using to betterthe proposed train the mode neuralls networkand simulation. used in theTen analysis, percent 5000of these load subscribers profiles were receive generated part ofusing their the energy proposed from models rooftop and photovoltaic simulation. panels Tenpercent and sell of surplus these subscribers generation receive power partto the of theirgrid throughenergy from the retail rooftop market. photovoltaic Using the panels initial and mass sell data surplus generated generation from power simulation to the to grid train through the SOM the neuralretail market. network Using does the not initial lead massto an data analyzable generated result. from One simulation of the toreasons train the is SOMthe high neural number network of elementsdoes not leadof the to input an analyzable matrix. Clustering result. One of of 15 the min reasons load curves is thehigh has little number conv ofergence elements in ofaddition the input to thematrix. high Clustering computational of 15 cost. min loadOn the curves other has hand, little sinc convergencee the curves in additionof the solar to theradiation high computational are available oncost. an Onhourly the otheraverage, hand, virtually since thea 15 curves min load of thecurve solar analysis radiation will are not available have a significant on an hourly effect average, on the accuracyvirtually aof 15 the min simulation. load curve analysisBy clustering will not the have mass-produced a significant e ffcurves,ect on thethe accuracyload behavior of the simulation.curves of non-PVBy clustering customers the mass-produced fall into 22 clusters curves, and the the load PV-c behavioronnected curves load profiles of non-PV fall customers into 26 clusters fall into with 22 differentclusters and characteristics the PV-connected as shown load in profiles Figure fall13. into 26 clusters with different characteristics as shown in Figure 13.

Figure 13. All cluster centers of mass data. Figure 13. All cluster centers of mass data. 5.5. Fraud Detection 5.5. FraudThe anomaliesDetection of power distribution networks fall into ﬁve categories: The anomalies of power distribution networks fall into five categories: 1. Malfunctioning meters. 1.2. MalfunctioningCustomers who meters. bypass the meter at certain hours. 3. Customers who consume part of their loads through an unmetered circuit at certain hours of the

day (Figure 14). 4. Subscribers who disable the meter on some days in each reading period (speciﬁc for old electromagnetic meters). 5. Customers who receive electricity from the grid across a circuit other than the meter and deliver it to the grid as photovoltaic energy. (This happens in cases where incentives are being made to buy renewable energy at a price higher than the cost of selling electricity to customers) (Figure 15). Energies 2020, 13, x FOR PEER REVIEW 18 of 24

Energies 2020, 13, x FOR PEER REVIEW 18 of 24 2. Customers who bypass the meter at certain hours. 2. 3. CustomersCustomers who who bypass consume the meterpart of at theircertain loads hours. thro ugh an unmetered circuit at certain hours of 3. Customersthe day (Figure who consume 14). part of their loads through an unmetered circuit at certain hours of 4. theSubscribers day (Figure who 14). disable the meter on some days in each reading period (specific for old 4. Subscriberselectromagnetic who disablemeters). the meter on some days in each reading period (specific for old 5. electromagneticCustomers who meters). receive electricity from the grid across a circuit other than the meter and 5. Customersdeliver it towho the receivegrid as photovoltaicelectricity from energy. the gr(Thisid across happens a circuitin cases other where than incentives the meter are andbeing delivermade itto to buy the renewable grid as photovoltaic energy at a energy. price higher (This thanhappens the cost in cases of selling where electricity incentives to arecustomers) being made(Figure to buy 15). renewable energy at a price higher than the cost of selling electricity to customers) (FigureEach of15). these types of anomaly leads to different behavior in the load profile curve and the amountEach ofof customers’these types energy of anomaly consumption. leads to Fordiffer exentample, behavior the consumption in the load curveprofile of curve customers and thewho amounthave defectiveof customers’ meters, energy while consumption. maintaining For exapproximatelyample, the consumption the behavioral curve patternof customers of normal who havecustomers, defective is higher meters, or lower;while or,maintaining in the case ofapproximately customers who the use behavioral conventional pattern meters of that normal cannot customers,be read online, is higher manipulating or lower; or, the in meter the case on ofa numbercustomers of whodays useper conventionalmeter reading meters period that will cannot reduce bethe read total online, energy manipulating measured. the meter on a number of days per meter reading period will reduce Energiesthe total2020 energy, 13, 1287 measured. 18 of 24

Metered Path Metered Path

Unmetered Path Unmetered Path

Figure 14. Illustration of energy theft through unmetered circuits. Figure 14. Illustration of energy theft through unmeteredunmetered circuits.circuits.

Insufficient Insufficientor disconnectedor disconnectedPV PV

Backdoor Backdoorcircuit circuit Figure 15. Illustration of energy fraud through energy selling. Figure 15. Illustration of energy fraud through energy selling. Each of these typesFigure of anomaly15. Illustration leads of toenergy diﬀerent fraud behaviorthrough energy in the selling. load proﬁle curve and the 5.5.1. Early Detection of Abnormalities/Fraud amount of customers’ energy consumption. For example, the consumption curve of customers who have5.5.1. defectiveEarlyFor customersDetection meters, of whilewho Abnormalities/Fraud maintaininguse conventional approximately electromagnetic the behavioral meters, pattern instantaneous of normal customers,data is not isavailable higherFor orcustomers and lower; the only or,who in accessible theuse case conventional ofdata customers is the electromagneticener whogy consumption use conventional meters, for a metersinstantaneous given period. that cannot Ancillarydata beis readnot data online,availablesuch manipulatingas andperiod the onlyof consumption, the accessible meter on data anumber number is the enerof of days daysgy consumption perof consumption, meter reading for a andgiven period postal period. will area reduce Ancillary (representing the totaldata energysuch as measured. period of consumption, number of days of consumption, and postal area (representing

5.5.1. Early Detection of Abnormalities/Fraud For customers who use conventional electromagnetic meters, instantaneous data is not available and the only accessible data is the energy consumption for a given period. Ancillary data such as period of consumption, number of days of consumption, and postal area (representing welfare level) are valuable data in this regard. In the city of Galougah’s network, in particular, the customers carefully monitored in these studies use either electromagnetic meters or digital meters not connected to the national smart metering system (FAHAM). The energy consumption data of these customers is available in different periods and years along with the test results of the meters. This information is valuable for evaluating the effectiveness of the present studies. To analyze anomalies/fraud in this subset of customers, mass energy consumption data is generated at different times with the time tag and used to train the SOM neural network. Then, real network data is used as test data. It is interesting to compare the results of the proposed method with the results of the meter inspection. Of the 82 customers evaluated, 14 were recognized as suspected of malformations. Table4 shows the comparison of the simulation result and the inspection result for the Energies 2020, 13, 1287 19 of 24 meters. The algorithm was not successful at detecting 2 of the actual frauds among target customers. This occurred due to similarity of the two customers to less energy-consuming customers. This error may be extinguished by adding some extra labels such welfare level to the ANN-network input data. There is also a mis-detection where a customer with no fraud was detected as suspected. This normally happens for customers with fully different consumption behavior of which load behavior cannot be assigned to any load clusters.

Table 4. Comparison of simulation results and test results for meters of study area.

Measurement Error The Calculated Value of the Meter Code Validation Result (Inspection Result) [%] Degree of Anomaly [1–9] 23***26 22% 4 Detected 23***39 8% 2 Detected 23***56 25% 4 Detected 23***94 9% 0 Not detected 23***22 27% 4 Detected 23***05 10% 3 Detected 23***27 16% 3 Detected 23***02 22% 0 Not detected 23***63 17% 3 Detected 23***16 81% 9 Detected 23***94 3% 3 Mis-detected 23***32 29% 6 Detected 24***80 25% 5 Detected 23***18 66% 7 Detected

5.5.2. Detection of Fraud in Customers Connected to AMI (Automatic Meter Reading) System No test data is available for this group of subscribers. Therefore, a deliberate anomaly is imposed on the consumption curve of these customers, to test the performance of the proposed method. Table5 describes the process and volume of deliberate anomalies created in the consumption data. The results of the fraud detection analysis for smartly metered customers are presented in Table6.

Table 5. Modeling anomaly of customers connected to smart meters.

Number of Frauding Type of Fraud Modeling Method Class of Anomaly Customers The customer bypasses the The customer’s load becomes 1% of PV and 1% of A meter at speciﬁed hours zero at random periods non-PV customers The customer consumes part of The customer’s load reaches 70% 1% of PV and 1% of his loads through an unmetered of normal load at random B non-PV customers circuit at certain hours periods A power supply with The customer sells the grid controllable power is considered C 1% of PV customers energy as PV energy on the load side

Table 6. Result of fraud detection analysis in customers with smart meters.

Percent of Percent of Average Degree of Average Detected Class of Anomaly Detected Mistakenly Anomaly in Degree of Anomaly Frauds Detected Frauds Reference Data in Records A 64 2.23 6 7 B 49 2.61 4 3 C 91 1.04 4 5

6. Conclusions The purpose of this study is to present a method for detecting fraud as the most important non-technical factor in distribution network losses. Distribution networks with high penetration of grid-connected photovoltaic sources have been specifically investigated in this study. Using Energies 2020, 13, 1287 20 of 24 a bottom-up model, the normal load behavior of customers is generated. Simulation is used to determine the effect of widespread use of grid-connected photovoltaic sources on the load profile of domestic customers. Load profile curves in the presence of grid-connected photovoltaic units are generated using simulation. Clustering of these curves using a self-organized neural network (SOM) determines normal load behavior patterns. Based on the fuzzy logic model, the Euclidean distance of any load profile to the center of the nearest normal cluster is calculated as the index of anomaly of the corresponding customer. The mechanism for detecting where the non-technical losses occur is different in networks with conventional electromagnetic meters to those in smart grids. A survey conducted to identify customers suspected of energy theft had successful results in both groups. The proposed algorithm has also shown great performance in detecting types of fraud in smart electrical networks, including: bypassing meters at specific hours, supplying part of the energy through an unmetered circuit, and selling non-photovoltaic energy as photovoltaic to the grid.

Author Contributions: Conceptualization, A.K. and A.V.; methodology, A.K. and H.M.; software, A.V.; validation, A.K.; formal analysis, A.K. and A.V.; investigation, A.V.; resources, A.A.; data curation, A.V.; writing—original draft preparation, A.V.; writing—review and editing, A.V., A.K..; visualization, A.V.; supervision, A.K., H.M., and A.A.; project administration, A.K.; All authors have worked on this manuscript together and all authors have read and approved the final manuscript. Funding: This research received no external funding. Conflicts of Interest: The authors declare no conflict of interest.

Nomenclatures

Pstart Probability of the appliance turning on at each time step A Indicator of home appliance ∆t Calculation time step h Time in hours f Frequency of appliance turning on in terms of number of times Pstep Scaling factor that scales probabilities on the basis of ∆t Io PV module output current Np Number of cells in parallel Ig Generated current by solar radiation Isat Reverse saturation current q Charge of an electron Vo PV module output voltage AD Diode ideality factor K The Boltzmann’s constant Tmod Temperature of the PV module in K Irsh Current due to intrinsic shunt resistance of the PV module Tr Reference temperature Ior Saturation current at reference temperature (Tr) Eg The band-gap energy It Short-circuit current temperature coeﬃcient Isc Short-circuit current of PV module Ns Number of cells in series Rsh Internal shunt resistance of the PV module Xi The ith input vector of neural network Wi,j The weight vector which connects the ith input to the jth output Dj A map unit Si The solar insolation Energies 2020, 13, 1287 21 of 24

Previous weight vector between input vector X and weight Wold i i,j vector to output neuron j new Wi,j Updated weight vector between input cell i and output cell j hi,j Neighboring function The distance of the ith load curve from the center of the jth D Li,j cluster t Time of the day PLi,t The load of the ith customer at time t

PCj,t The load of the center of the jth cluster at time t nc The number of clusters µi,j The membership of any customers to normal behavior Pnom Nominal power of each appliance [W] Pstandby Standby power of each appliance [W] napp Number of appliances in each home tcycle The average time period that each appliance keeps on RMSEnorm Normalized root mean square error MAEnorm Normalized mean absolute error MRE Relative mean error e Values obtained from simulation m Values obtained from measurement y Number of values

References

1. TAVANIR. Detailed Statistics on Iran’s Power Distribution Networks in 1396; TAVANIR: Tehran, Iran, 2018; Volume 1. 2. Cabral, J.; Gontijo, E.M. Fraud detection in electrical energy consumers using rough sets. In Proceedings of the 2004 IEEE International Conference on Systems, Man and Cybernetics, Hague, The Netherlands, 10–13 October 2004; pp. 3625–3629. 3. Cabral, J.E.; Pinto, J.O.; Pinto, A.M. Fraud detection system for high and low voltage electricity consumers based on data mining. In Proceedings of the 2009 IEEE Power & Energy Society General Meeting, Calgary, AB, Canada, 26–30 July 2009; pp. 1–5. 4. Monedero, I.; Biscarri, F.; Leon, C.; Biscarri, J.; Millan, R. MIDAS: Detection of Non-Technical Losses in Electrical Consumption Using Neural Networks and Statistical Techniques. Comput. Vis. 2006, 3984, 725–734. 5. Viegas, J.; Esteves, P.R.; Melicio, R.; Mendes, V.; Vieira, S.M. Solutions for detection of non-technical losses in the electricity grid: A review. Renew. Sustain. Energy Rev. 2017, 80, 1256–1268. [CrossRef] 6. Han, W.; Xiao, Y. NFD: Non-technical loss fraud detection in smart grid. Comput. Secur. 2017, 65, 187–201. [CrossRef] 7. Abaide, A.; Canha, L.; Barin, A.; Cassel, G. Assessment of the smart grids applied in reducing the cost of distribution system losses. In Proceedings of the 2010 7th International Conference on the European Energy Market, Madrid, Spain, 23–25 June 2010; Institute of Electrical and Electronics Engineers (IEEE): Piscataway, NJ, USA; pp. 1–6. 8. Jiang, R.; Lu, R.; Wang, Y.; Luo, J.; Shen, C.; Shen, X. Energy-theft detection issues for advanced metering infrastructure in smart grid. Tsinghua Sci. Technol. 2014, 19, 105–120. [CrossRef] 9. Mashima, D.; Cárdenas, A.A. Evaluating Electricity Theft Detectors in Smart Grid Networks. In International Workshop on Recent Advances in Intrusion Detection; Springer: Berlin/Heidelberg, Germany, 2012; Volume 7462, pp. 210–229. 10. Dickert, J.; Schegner, P. Residential load models for network planning purposes. In Proceedings of the 2010 Modern Electric Power Systems, Wroclaw, Poland, 20–22 September 2010; pp. 1–6. 11. Nickel, D.; Braunstein, H. Distribution transformer loss evaluation: II-load characteristics and system cost parameters. IEEE Trans. Power Appar. Syst. 1981, 2, 798–811. [CrossRef] 12. Capasso, A.; Grattieri, W.; LaMedica, R.; Prudenzi, A. A bottom-up approach to residential load modeling. IEEE Trans. Power Syst. 1994, 9, 957–964. [CrossRef] Energies 2020, 13, 1287 22 of 24

13. Chuan, L.; Ukil, A. Modeling and validation of electrical load profiling in residential buildings in Singapore. IEEE Trans. Power Syst. 2014, 30, 2800–2809. [CrossRef] 14. Gao, B.; Liu, X.; Zhu, Z. A bottom-up model for household load profile based on the consumption behavior of residents. Energies 2018, 11, 2112. [CrossRef] 15. Gruber, J.; Jahromizadeh, S.; Prodanovic, M.; Rakoˇcević,V. Application-oriented modelling of domestic energy demand. Int. J. Electr. Power Energy Syst. 2014, 61, 656–664. [CrossRef] 16. Gils, H.C. Assessment of the theoretical demand response potential in Europe. Energy 2014, 67, 1–18. [CrossRef] 17. Munkhammar, J.; Rydén, J.; Widén, J. Characterizing probability density distributions for household electricity load profiles from high-resolution electricity use data. Appl. Energy 2014, 135, 382–390. [CrossRef] 18. Swan, L.G.; Ugursal, V.I. Modeling of end-use energy consumption in the residential sector: A review of modeling techniques. Renew. Sustain. Energy Rev. 2009, 13, 1819–1835. [CrossRef] 19. Paatero, J.; Lund, P. A model for generating household electricity load profiles. Int. J. Energy Res. 2006, 30, 273–290. [CrossRef] 20. Widén, J.; Lundh, M.; Vassileva, I.; Dahlquist, E.; Ellegård, K.; Wäckelgård, E. Constructing load profiles for household electricity and hot water from time-use data—Modelling approach and validation. Energy Build. 2009, 41, 753–768. [CrossRef] 21. Widén, J.; Munkhammar, J. Evaluating the benefits of a solar home energy management system: Impacts on photovoltaic power production value and grid interaction. In Proceedings of the ECEEE 2013 Summer Study, Presqu’île de Giens, France, 3–8 June 2013. 22. Widén, J.; Molin, A.; Ellegård, K. Models of domestic occupancy, activities and energy use based on time-use data: Deterministic and stochastic approaches with application to various building-related simulations. J. Build. Perform. Simul. 2012, 5, 27–44. [CrossRef] 23. Richardson, I.; Thomson, M.; Infield, D. A high-resolution domestic building occupancy model for energy demand simulations. Energy Build. 2008, 40, 1560–1566. [CrossRef] 24. Richardson, I.; Thomson, M.; Infield, D.; Delahunty, A. Domestic lighting: A high-resolution energy demand model. Energy Build. 2009, 41, 781–789. [CrossRef] 25. Widén, J.; Nilsson, A.M.; Wäckelgård, E. A combined Markov-chain and bottom-up approach to modelling of domestic lighting demand. Energy Build. 2009, 41, 1001–1012. [CrossRef] 26. Widén, J.; Wäckelgård, E. A high-resolution stochastic model of domestic activity patterns and electricity demand. Appl. Energy 2010, 87, 1880–1892. [CrossRef] 27. Richardson, I.; Thomson, M.; Infield, D.; Clifford, C. Domestic electricity use: A high-resolution energy demand model. Energy Build. 2010, 42, 1878–1887. [CrossRef] 28. Kavgic, M.; Mavrogianni, A.; Mumovic, D.; Summerfield, A.; Stevanovic, Z.; Djurovic-Petrovic, M. A review of bottom-up building stock models for energy consumption in the residential sector. Build. Environ. 2010, 45, 1683–1697. [CrossRef] 29. Omran, W.A.; Kazerani, M.; Salama, M.M.A. Investigation of methods for reduction of power fluctuations generated from large grid-connected photovoltaic systems. IEEE Trans. Energy Convers. 2010, 26, 318–327. [CrossRef] 30. Datta, M.; Senjyu, T.; Yona, A.; Funabashi, T.; Kim, C.-H. A frequency-control approach by photovoltaic generator in a PV–diesel hybrid power system. IEEE Trans. Energy Convers. 2010, 26, 559–571. [CrossRef] 31. Abdolzadeh, M.; Zarei, T. Optical and thermal modeling of a photovoltaic module and experimental evaluation of the modeling performance. Environ. Prog. Sustain. Energy 2016, 36, 277–293. [CrossRef] 32. Houari, Z.M.; Zohra, Z.F.; Mansour, Z.; Amar, T. Photovoltaic solar array: Modeling and output power optimization. Environ. Prog. Sustain. Energy 2016, 35, 1529–1536. [CrossRef] 33. Lokesh, T.; Srinivasa, D.; Srinath, M.S. Review on MPPT techniques for solar PV array system. Our Herit. 2020, 68, 7887–7894. 34. Singh, B.P.; Goyal, S.K.; Siddiqui, S.A. Analysis and Classification of Maximum Power Point Tracking (MPPT) Techniques: A Review. In Lecture Notes in Electrical Engineering; Springer: Berlin/Heidelberg, Germany, 2019; pp. 999–1008. 35. Mahdi, A.S.; Mahamad, A.K.; Saon, S.; Tuwoso, T.; Elmunsyah, H.; Mudjanarko, S.W. Maximum power point tracking using perturb and observe, fuzzy logic and ANFIS. SN Appl. Sci. 2019, 2, 89. [CrossRef] Energies 2020, 13, 1287 23 of 24

36. Ahmed, J.; Chin, V.J. An improved perturb and observe (P&O) maximum power point tracking (MPPT) algorithm for higher efficiency. Appl. Energy 2015, 150, 97–108. 37. Sera, D.; Mathe, L.; Kerekes, T.; Spataru, S.; Teodorescu, R. On the Perturb-and-Observe and Incremental Conductance MPPT Methods for PV Systems. IEEE J. Photovolt. 2013, 3, 1070–1078. [CrossRef] 38. De Brito, M.A.; Sampaio, L.P.; Luigi, G.; Melo, G.A.; Canesin, C.A. Comparative analysis of MPPT techniques for PV applications. In Proceedings of the 2011 International Conference on Clean Electrical Power (ICCEP), Ischia, Italy, 14–16 June 2011; pp. 99–104. 39. Pourgharibshahi, H.; Abdolzadeh, M.; Fadaeinedjad, R. Verification of computational optimum tilt angles of a photovoltaic module using an experimental photovoltaic system. Environ. Prog. Sustain. Energy 2014, 34, 1156–1165. [CrossRef] 40. Raj, M.P.; Joshua, A.M. Design, implementation and performance analysis of a LabVIEW based fuzzy logic MPPT controller for stand-alone PV systems. In Proceedings of the 2017 IEEE International Conference on Power, Control, Signals and Instrumentation Engineering (ICPCSI), Chennai, India, 21–22 September 2017; pp. 1012–1017. 41. Boumaaraf, H.; Talha, A.; Bouhali, O. A three-phase NPC grid-connected inverter for photovoltaic applications using neural network MPPT. Renew. Sustain. Energy Rev. 2015, 49, 1171–1179. [CrossRef] 42. Ramaprabha, R.; Mathur, B. Genetic algorithm based maximum power point tracking for partially shaded solar photovoltaic array. Int. J. Res. Rev. Inf. Sci. 2012, 2, 161–163. 43. Ishaque, K.; Chin, V.J.; Amjad, M.; Mekhilef, S. An Improved Particle Swarm Optimization (PSO)–Based MPPT for PV with Reduced Steady-State Oscillation. IEEE Trans. Power Electron. 2012, 27, 3627–3638. [CrossRef] 44. Atiq, J.; Soori, P.K. Modelling of a grid connected solar PV system using MATLAB/Simulink. Int. J. Simul. Syst. Sci. Technol. 2017, 17, 451–457. 45. Fayyad, U.; Piatetsky-Shapiro, G.; Smyth, P. From data mining to knowledge discovery in databases. Al Mag. 1996, 17, 37. 46. Piatetsky-Shapiro, G. Knowledge discovery in real databases: A report on the IJCAI-89 Workshop. Al Mag. 1990, 11, 68. 47. Cabral, J.E.; Pinto, J.O.P.; Martins, E.M.; Pinto, A.M.A.C. Fraud detection in high voltage electricity consumers using data mining. In Proceedings of the 2008 IEEE/PES Transmission and Distribution Conference and Exposition, Chicago, IL, USA, 21–24 April 2008; Institute of Electrical and Electronics Engineers (IEEE): Piscataway, NJ, USA; pp. 1–5. 48. Alvarez-Guerra, E.; Molina, A.; Viguri, J.; Alvarez-Guerra, M. A SOM-based methodology for classifying air quality monitoring stations. Environ. Prog. Sustain. Energy 2010, 30, 424–438. [CrossRef] 49. Orsi Noor Consultant Engineers, O.N.C. Mazandaran Galougah Power Distribution Network Master Planning-Load Modelling. In Engineering; Mazandaran Power Distribution Co.: Amir Mazandarani, Iran, 2017; Volume 01. 50. Orsi Noor Consultant Engineers, O.N.C. Mazandaran Galougah Power Distribution Network Master Planning-Load Forecasting. In Engineering; Mazandaran Power Distribution Co.: Amir Mazandarani, Iran, 2017; Volume 01. 51. SATBA. Share of Household Energy Consumption; Eurostat: Brussels, Belgium, 2013. 52. Laicane, I.; Blumberga, D.; Blumberga, A.; Rosa, M. Evaluation of Household Electricity Savings. Analysis of Household Electricity Demand Profile and User Activities. Energy Procedia 2015, 72, 285–292. [CrossRef] 53. Engineers, O.N.C. Modern Engineering and Technology Development Studies: Engineering Studies on Development, Modification and Optimization of Mazandaran Power Distribution Networks. In Engineering; Mazandaran Power Distribution Co.: Amir Mazandarani, Iran, 2019; Volume 01. 54. Kasaeian, A.; Barghamadi, H.; Pourfayaz, F. Performance comparison between the geometry models of multi-channel absorbers in solar volumetric receivers. Renew. Energy 2017, 105, 1–12. [CrossRef] Energies 2020, 13, 1287 24 of 24

55. Poulek, V.; Matuska, T.; Libra, M.; Kachalouski, E.; Sedláˇcek,J. Inﬂuence of increased temperature on energy production of roof integrated PV panels. Energy Build. 2018, 166, 418–425. [CrossRef] 56. Libra, M.; Beránek, V.; Sedláˇcek,J.; Poulek, V.; Tyukhov, I. Roof photovoltaic power plant operation during the solar eclipse. Sol. Energy 2016, 140, 109–112. [CrossRef]

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).